New model of reactive transport in a single-well push–pull test with aquitard effect and wellbore storage

Wang, Quanrong; Wang, Junxia; Zhan, Hongbin; Shi, Wenguang

doi:10.5194/hess-24-3983-2020

Cited by 14 publications

(19 citation statements)

References 44 publications

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“…In the case of the inverse Goldstein‐Weber transformation, a numerical integration formula based on the Bessel function was used, which is simple to implement and has a high degree of accuracy. Regarding the inverse Laplace transform, the Stehfest method (Wang et al 2020a; Wang et al 2020b) was used to perform the inversion of the semi‐analytical solution as presented in Equations 25 through 30. To facilitate the computation, we developed a MATLAB program, which is available from the authors upon request.…”

Section: Methodsmentioning

confidence: 99%

A Novel Semi‐Analytical Solution of Over‐Damped Slug Test in a Three‐Layered Aquifer System

Cao,

Wen,

Chen

et al. 2023

Groundwater

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The slug test has been commonly used to estimate aquifer parameters. Previous studies on the slug test mainly focused on a single‐layer aquifer. However, understanding the interaction between layers is particularly important when assessing aquifer parameters under certain circumstances. In this study, a new semi‐analytical model on transient flow in a three‐layered aquifer system with a partially penetrating well was developed for the slug test. The proposed model was solved using the Laplace transform method and the Goldstein‐Weber transform method, where the semi‐analytical solution for the model was obtained. The drawdowns of the proposed model were analyzed to understand the impacts of the different parameters on the drawdowns in a three‐layered aquifer system. The results indicated that groundwater interactions between the layers have a significant impact on the slug test. In addition, a shorter and deeper well screen as well as a greater permeability ratio between the layers creates a greater interface flow between them, leading to a higher drawdown in the slug test. Finally, a slug test in a three‐layered aquifer system was conducted in our laboratory to validate the new model, which indicated that the proposed model performed better in the interpretation of the experimental data than a previous model proposed by Hyder et al. (1994). We also proposed an empirical relationship to qualitatively identify the errors in the application of single‐layer model for the analysis of response data in a three‐layered aquifer system.

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Section: Methodsmentioning

confidence: 99%

A Novel Semi‐Analytical Solution of Over‐Damped Slug Test in a Three‐Layered Aquifer System

Cao,

Wen,

Chen

et al. 2023

Groundwater

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“…The integral transform technique involves using integral transforms such as Laplace or Fourier transforms to convert the ADE into an algebraic equation, which can be solved using inverse transforms (Cotta, 1993;Guerrero et al, 2009). A variety of integral transforms have been obtained in many previous investigations, and this method has been successfully applied to many problems in hydrology and environmental science (Cotta, 1993;Guerrero et al, 2009;Y.-F. Lin et al, 2022;Mikhailov & Özişik, 1984;Wang et al, 2020;Zhu & Wen, 2019). For instance, Mikhailov and Özişik (1984) reviewed and classified the integral transform techniques for solving linear diffusion problems, and showed numerous applications in the field of heat and mass transfer.…”

Section: Mathematical Modelmentioning

confidence: 99%

A Two‐Dimensional Closed‐Form Analytical Solution for Heat Transport With Nonvertical Flow in Riparian Zones

Shi

Zhan

Wang

et al. 2023

Water Resources Research

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Heat as a tracer has received increasing attention in recent decades and has become a popular and widely used tool for quantifying streambed fluxes, among many other applications. Nonvertical flow component is an important parameter for heat transport in riparian zones. However, previous investigations using heat as a tracer in the quantification of streambed fluxes frequently overlooked or simplified nonvertical flow component with erroneous presumptions. In this study, a novelty two‐dimensional closed‐form analytical solution for heat transport with vertical and nonvertical flow components and arbitrary initial and boundary conditions under losing conditions is presented for the first time using Green’s function method. The new model is tested by finite‐element solution and stochastic modeling. The capabilities of the new analytical solution are demonstrated using field data. Results show that the nonvertical flow component has a significant impact on heat transport in streambed. The temperature difference between the streambed and the surface water increases as the nonvertical flow component increases, and the amplitude of the temperature curves decreases with increasing horizontal distance from the center of stream at the same depth due to the influences of nonvertical flow. Stochastic modeling shows that an increasing nonuniform flow can result in overestimation of vertical and nonvertical flow components near the bank of stream, and the new analytical model works well in a heterogeneous streambed when the variance of natural logarithm of the streambed hydraulic conductivity is less than 0.10 (). The vertical and nonvertical flow components are more sensitive to temperature‐time data than the other parameters. The new analytical model is a significant advancement of the previous one‐dimensional analytical models which only considered vertical flow.This article is protected by copyright. All rights reserved.

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“…There are several numerical inverse Laplace transform methods available, such as the Stehfest method (Stehfest and Harald, 1970a;Stehfest and Harald, 1970b), the Schapery method (Schapery, 1962), the Fourier series method (Dubner and Abate, 1968), and so on. The Stehfest method was demonstrated to perform well in solving the problems related to solute transport (Wang et al, 2020a;Wang et al, 2020b), and will be employed to conduct the inverse Laplace transform on Eqs. ( 8) -( 9) in this study.…”

Section: Solutions In Real-time Domainmentioning

confidence: 99%

“…There are two types of treatments. First, the aquifer horizontal extension was assumed to be infinite (Rezaei et al, 2016;Singh et al, 2020;Wang et al, 2020b). Such assumption performs well for the cases that the aquifer is long enough or the experimental time is short enough that tracer could not arrive in outlet boundary.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Analytical Model of Solute Transport in an Aquifer-Aquitard System with Mixing Processes in the Reservoirs

Shi

Wang

2022

Preprint

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Analytical models have been widely used to aid understanding the physical and chemical processes of tracer (or chemicals) in an aquifer-aquitard system in the laboratory-controlled experiment, when the observation data is few or not available during the experiment. When injecting tracer into (or extracting them from) the aquifer-aquitard system during experiments, the pre-inlet and after-outlet reservoirs are indispensable. However, the concentration variation in the reservoirs was not treated properly in previous analytical models, resulting in poor performance in interpreting experimental data. In this study, new mathematical models describing the concentration variation in the pre-inlet and the after-outlet reservoirs are proposed, and they are integrated into the novel analytical model. The novel analytical model is developed under the mobile-immobile (MIM) framework in the aquifer-aquitard system, considering the longitudinal and vertical dispersion, the advection, and the first-order chemical reaction in both aquifer and aquitard. A finite-difference solution is developed and the experimental data are employed to test the new analytical model. Results indicate that the concentration variation in the reservoirs is important to solute transport in the aquifer-aquitard system in the laboratory-controlled experiment, and the new analytical model outperforms the previous models in interpreting experimental data. The global sensitivity analysis demonstrates that the output concentration of solute transport in the aquifer-aquitard system is most sensitive to the volume of water in the pre-inlet reservoir. The contribution of the diffusion effect to the total mass flux of tracer crossing the aquifer-aquitard interface is much smaller than the contribution of the dispersive and advective effects.

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New model of reactive transport in a single-well push–pull test with aquitard effect and wellbore storage

Cited by 14 publications

References 44 publications

A Novel Semi‐Analytical Solution of Over‐Damped Slug Test in a Three‐Layered Aquifer System

A Novel Semi‐Analytical Solution of Over‐Damped Slug Test in a Three‐Layered Aquifer System

A Two‐Dimensional Closed‐Form Analytical Solution for Heat Transport With Nonvertical Flow in Riparian Zones

A Novel Analytical Model of Solute Transport in an Aquifer-Aquitard System with Mixing Processes in the Reservoirs

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